Based on density functional theory (DFT) together with the projector augmented wave (PAW) method, we systematically investigate the structural, magnetic and electronic properties of the chalcogenide MnTe in six competing structures: rocksalt (RS), cesiun-chloride (CC), zinc-blende (ZB), wurtzite (WZ), iron-silicide (IS) and nickel-arsenide (NA). The ground state of MnTe is completely determined. And the structural parameters, magnetic properties, bulk modulus, phase transition pressure, and the density of states are studied, too. The density of states shows that MnTe in RS, CC and IS structures are antiferromagnetic conductors, and MnTe in WZ, ZB and NA are antiferromagnetic semiconductors. These results provide us the possibility to apply them to the spintronics of antiferromagnetic systems.